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  • Find the minimum value of the function f(x)=3^[(x^2-2)^3 +8]

Find the minimum value of the function f(x)=3^[(x^2-2)^3 +8]

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Solution:    We have ,    

                     f(x)=3^(x^2-2)^3+8

        The  function   f(x)=3^phi (x)  takes on the minimum value at the 

         same point  as the function phi (x).

      Hence ,   

                       phi (x)=x^6-6x^4+12x^2=x^2[(x^2-3)^2+3].

  Whence it is clear that the funtion phi (x) attains the minimum value 

at x=0 . that is why the minimum value of the function  f(x) is 

equal to 3^0=1

Posted by

Deependra Verma

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